Bound State Solutions of the Dirac Equation in the Extreme Kerr Geometry

Abstract

In this paper we consider bound state solutions, i.e., normalizable time-periodic solutions of the Dirac equation in the exterior region of an extreme Kerr black hole with mass $M$ and angular momentum $J$. It is shown that for each azimuthal quantum number $k$ and for particular values of $J$ the Dirac equation has a bound state solution, and that the energy of this Dirac particle is uniquely determined by $\omega =-\frac{kM}{2J}$. Moreover, we prove a necessary and sufficient condition for the existence of bound states in the extreme Kerr-Newman geometry, and we give an explicit expression for the radial eigenfunctions in terms of Laguerre polynomials.

17 pages, 3 figures, small corrections and improvements

References in corpus (1)

• Non-Existence of Time-Periodic Solutions of the Dirac Equation in an Axisymmetric Black Hole Geometry

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